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Simplifying x3 + -10x2 + 5x = 0 Reorder the terms: 5x + -10x2 + x3 = 0 Solving 5x + -10x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -10x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + -10x + x2)' equal to zero and attempt to solve: Simplifying 5 + -10x + x2 = 0 Solving 5 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -10x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10x + x2 = 0 + -5 -10x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10x + x2 = -5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -5 + 25 Reorder the terms: 25 + -10x + x2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10x + x2 = 20 Factor a perfect square on the left side: (x + -5)(x + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -5 = 4.472135955 Simplifying x + -5 = 4.472135955 Reorder the terms: -5 + x = 4.472135955 Solving -5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.472135955 + 5 x = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 x = 9.472135955 Simplifying x = 9.472135955Subproblem 2
x + -5 = -4.472135955 Simplifying x + -5 = -4.472135955 Reorder the terms: -5 + x = -4.472135955 Solving -5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.472135955 + 5 x = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 x = 0.527864045 Simplifying x = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.472135955, 0.527864045}Solution
x = {0, 9.472135955, 0.527864045}
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